There is no rule for immunity, but it is not required
The official books do not describe creatures that are explicitly immune to this particular action from this particular statistic block. That does not mean there are no such creatures in your game world. On the contrary, the Monster Manual suggests not limiting the DM by:
Of course you can do whatever you want with these monsters. Nothing we say here is intended to limit your creativity.
So, as a DM, if you think it's absurd to fill your game world with ubiquitous shadows, do not do that, The book also specifies what these descriptions are for:
Maybe you're reading a monster's entry and you're spurring on an adventure that revolves around it, or you have a great idea for a dungeon and you need exactly the right monsters to populate it. Here is the Monster Handbook.
In other words, Monster Manual descriptions should be used to make exciting encounters for the party or to generate ideas for a story. They should not be used as a limitation for the wordbuilding processand serves as a kind of basic "laws of nature." A dulling shadow is a decent challenge for the group, and it should stay that way.
This will probably happen outside the screen as well
If something happens off-screen in your games, it's like DM Not should use standard combat rules to solve the result. If 100 city dwellers have killed a dragon somewhere, you can describe this as plausibly as you think fit. Do not fight 101 players, especially not in the middle of your game, so players wait meaninglessly.
The standard combat rules should be used to simulate small encounters. Use mechanics suitable for resolution or none if not required. There are mass-fight rules for large armies (currently only for UA), but they are exaggerated to solve something that has happened somewhere before.
DMG Chapter 8 "Running the Game" describes rules as a DM tool:
Rules allow you and your players to have fun at the table. The rules are for you, not the other way around.
If something (like following a literal reading of a rule) makes your world stupid or absurd and spoils the fun, do not do that. So the rules should be applied according to the rules themselves.